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Triangular embeddings of complete graphs from graceful labellings of paths

Goddyn, Luis; Richter, R. Bruce and Širáň, Jozef (2007). Triangular embeddings of complete graphs from graceful labellings of paths. Journal of Combinatorial Theory, Series B, 97(6) pp. 964–970.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1016/j.jctb.2007.02.009
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Abstract

We show that to each graceful labelling of a path on 2s+1 vertices, s≥2, there corresponds a current assignment on a 3-valent graph which generates at least 22s cyclic oriented triangular embeddings of a complete graph on 12s+7 vertices. We also show that in this correspondence, two distinct graceful labellings never give isomorphic oriented embeddings. Since the number of graceful labellings of paths on 2s+1 vertices grows asymptotically at least as fast as (5/3)2s, this method gives at least 11s distinct cyclic oriented triangular embedding of a complete graph of order 12s+7 for all sufficiently large s.

Item Type: Journal Article
Copyright Holders: 2007 Elsevier Inc.
ISSN: 0095-8956
Keywords: graceful labelling; path; triangulation; complete graph; cyclic
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 23264
Depositing User: Jozef Širáň
Date Deposited: 24 Sep 2010 15:09
Last Modified: 02 Dec 2010 21:06
URI: http://oro.open.ac.uk/id/eprint/23264
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